TEWKSBURY — The family feud that has brought the Market Basket supermarket chain to its knees may be nearing its end.

Ousted CEO Arthur T. Demoulas has reportedly made a $1.5 billion offer to buy out the part of the company controlled by his rival cousin, Arthur S. Demoulas, and his allies on the board.

The board was scheduled to meet Sunday but the meeting was called off die to disagreements over some terms of the sale.

Arthur T. Demoulas' ouster earlier this summer prompted an employee walkout and customer boycott that has led to empty shelves and a mere trickle of business at the private company's 71 stores in Massachusetts, New Hampshire and Maine.

Store managers and employees expressed confidence over the weekend that a deal was imminent.